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It was announced on Thursday that Abramovich had been added to the UK's sanction list following Russia's invasion of neighbouring Ukraine.
Abramovich announced his intentions to sell the club last week, but no buyer was found and it'll have huge consequences for the reigning world champions.
Carragher believes it could have a huge impact on current manager Tuchel's future and has suggested United should get in contact.
"Manchester United have been presented with the ideal opportunity to recruit the manager who should be their number one target: Thomas Tuchel," Carragher explained in his column for The Telegraph.
"Given the events at Chelsea, United’s decision to wait until the end of the season presents them with a choice no-one could have foreseen. One of the best managers in the world – the current FIFA coach of the year – must be top of their list.
"Tuchel, like everyone else at Stamford Bridge, will have no idea what the future holds at his current club.
"No-one can offer him any assurances about how the squad will look at the start of next season given the club’s sale is on hold.
"No manager wants to be working amid such a background of uncertainty. If he gets the chance to leave for a club of United’s stature, he must take it.
"United can offer him the security and backing every top coach craves. Yes, it will seem a predatory move – taking advantage of Chelsea’s crisis – but from United and Tuchel’s perspective the more you consider it, the more of a no-brainer it is."
United are currently in the hunt for a new permanent manager after sacking Ole Gunnar Solskjaer in November.
Ralf Rangnick is in charge on an interim basis until the end of this season, when the Red Devils will pick a long-term boss.
Chelsea are allowed to continue playing games due to their standing as a 'significant cultural asset', but only existing ticket holders can attend games.
The Blues are also unable to sign players or renew contracts of playing staff.
Defensive trio Andreas Christensen, Antonio Rudiger and Cesar Azpilicueta's contracts are set to expire at the end of this season.